Two major advantages of the approach in this paper are that it does not require reparameterization of the manifold and that it uses GFI to define a posterior-like distribution on the (constrained) parameter space that is coordinate-invariant and does not require one to choose a subjective prior distribution. GFI is already a strong method for inference on manifolds; as pointed out in [1]}, the generalized fiducial distribution (GFD) is invariant to the choice of parameterization. We generalize this invariance by showing that, in the constrained case, the GFD defined according to a reparameterization of the manifold (when a reparameterization is known) is equivalent to our method, which defines the GFD on (REF ) only using \(g\) . This development, called the constrained generalized fiducial distribution (CGFD), inherits many of the desired qualities of the original GFD, such as asymptotic exactness of the fiducial confidence sets and desirable coverages, which are illustrated in data simulations in the sections following.
